I assume you are wanting to rent a furnished studio apartment.
I have used one agency for three separate trips: "A Part of Paris". The owner, Joanna Viltart, is trustworthy and reliable. For example, the deposit has always been returned once with a reasonable reduction for something I broke.
You can use the A Part of Paris website to search. Just click on All Districts, Apartment Type and Available Dates. The website search is useful to get an idea of pricing and to help narrow down what features you want. For example: I choose not to be too many floors up and want a clothes washer. I believe on every trip, even after doing my search, I have ended up taking a different apartment based on Joanna's advice.
One final thought: Most of the apartments offered by A Part of Paris are in the 3rd arrondissement which is my favorite. You can walk to the Seine in the afternoons, there are plenty of grocery stores, markets, bars, and inexpensive places to eat. Big plus: You aren't in the more touristy arrondissements like the fourth and fifth.
Good luck! Have a safe stay.